Even on Windows, using the registry is overkill. You can do the following:
Open up preferences (Cmd-,) and select the "Documents" category. Here you will find "Documents in recently used list", change this number to 1. This will get rid of all but the last opened document. Then open some document that can remain in the list (e.g. go to http://samplepdf.com and download the sample and open it). Then go back to preferences and adjust the number of documents you want it to be able to see in the list.
This also works on Windows.
If you really want to get rid of the list without having to go into preferences twice, this information is also stored in the comadobe.Acrobat.Pro.plist file (as 11>AVGeneral>Recent Files). But as usual with editing system files, don't be surprised if things don't work anymore after you make a change. The format of this file is not documented (the same for the Windows registry), and we don't know what can be safely removed from the file.
Karl Heinz Kremer
PDF Acrobatics Without a Net
PDF Software Development, Training and More...
http://www.khkonsulting.com